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METRIC SYSTEM

Learn about the metric system, its base units, prefixes, and how to convert between different units using the factor label method.

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METRIC SYSTEM

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  1. METRIC SYSTEM

  2. Measuring Systems were confusing!!!Everyone used a different method!!We did not speak same language!!Could Not trade!!

  3. Mars Craft Explodes!!

  4. Developed Metric System • French govt came up with it. • Formed in 1799 • Designed easiest system • Simple Decimal based system • All units divisible by 10 • Called Système International d'Unités (or SI for short)

  5. Who uses it??? • Every country but US • (and Myanmar and Liberia) • US Slowly converting over to using it • SCIENTISTS ALWAYS USE IT!!!

  6. METRIC BASE UNITS • Length = Meter, m • Time = Seconds, sec • Volume = liters, L • Mass = grams, g • Weight = Newtons, N

  7. METRIC Prefixes Prefixes tell you how many of the base unit are present Examples: Kilo- means 1000 (kilometer literally means “1000 meters”) Centi- means 1/100 (one hundredth) (Centimeter literally means “1/100 of a meter”)

  8. Metric System • Giga- 1 billion base • Mega- 1 million base • Kilo – 1 thousand base • Standard – base unit (meter, liter, etc) • Deci – 1/10th of base • Centi – 1/100th of base • Milli – 1/1000th of base • Micro – 1 millionth of base • Nano – 1 billionth of base

  9. Common Metric Prefixes Unit Multiples 100 hecto -- 0.01 10 kilo 1,000 deca -- (base unit) deci 0.1 centi milli 0.001

  10. Move decimal places using step ladder King Hector Doesn’t Usually Drink Chocolate Milk kilo Hecto Deka base unit deci Centi Milli

  11. Convert these on your own… 5 m = ________________________cm 1300 mm = _______________________m 15 km = _________________________ m 12 km = _________________________ mm 270 cm = ________________________m 14500 cm = _______________________ km

  12. How did you do??? 5 m = 500 cm 1300 mm = 1.3 m 15 km = 15,000 m 12 km = 12,000,000 mm 270 cm = 2.7 m 14500 cm = 0.145 km

  13. Memorize Conversion Factors • 1000 meters in 1 kilometer • 3600 seconds in 1 hour • 1600 meters in 1 mile

  14. METRIC REVIEW32 cm = 0.32 m762 mm = 0.762m3.6 km = 3600m63 ns = 0. 00063 s25 ms = 0.025 s350 km = 3.5 e 5 or 350,00052.3 cm = 0.523 m

  15. 0.432 mm = 0.000432 m or 4.32 e –4 400 g = 0.4 kg16.9 mg = 0. 0000169 or 1.69 e –555 g = 0.055 kg5,000,000 mg = 5 kg5275 g = 5.275 kg0.425 g = 4.25 e –4 kg4.25 mg = 4.25 e –6 kg

  16. RhodZ’s Picket Fencing

  17. Factor Label Method AKA : Dimensional Analysis

  18. Why is factor label important? • Factor label method allows us to solve problems that seem more difficult by breaking the problem down into parts. • Factor label becomes very important when it is harder to convert quantities.

  19. Important Ideas to Remember… • The key to factor label is the cancellation of units. • Always identify the known, unknown, and conversion factors in the problem. • Only one number and one unit per box!!!!! • Like units are always diagonal from one another. • Unknown is placed in first column. The rest of the columns are conversion factors. • m/s km/h mph are all fractional units!!! • Important Conversion factors: 1000 meters in 1 km and 3600 seconds in 1 hour

  20. Step One • Determine your known, unknown, and the conversion factors needed. • Known = what you start with in the problem, the given • Unknown = what you are solving for, ? • Conversion factors= memorized proportions or fractions that demonstrate how much of one unit is in another unit of measure. Ex: 12 eggs in a dozen. 3 ft in a yard. 1000 m in a km….Etc…

  21. Our Example… How many pumpkins are in 20 pumpkin patches, if there are 25 pumpkins in one pumpkin patch? • Known = 20 pumpkin patches • Unknown = pumpkins • Conversion factors = 25 pumpkins 1 pumpkin patch

  22. Step Two • Set up the factor label “fence” = *** note If using more than one conversion factor, you will need more fence posts***

  23. Step Three • Put Known with its units in first bracket. 20 pumpkin patches = One number and 1 unit per box!!!!!!

  24. Step Four • Place conversion factor in next bracket. • Make sure when you use conversion factors, the known units are diagonal so you can cancel out the units that you want to eliminate. 20 pumpkin patches 25 pumpkins = 1 pumpkin patch Like units are always diagonal!!!

  25. Step Five • Multiply across the top. Multiply across the bottom. • Cancel units. 20 pumpkin patches 25 pumpkins = 500 pumpkins 1 pumpkin patch 1

  26. See the cancellation? • 20 pumpkin patches X 25 pumpkins = 500 pumpkins • 1 pumpkin patch Like units have to be DIAGONAL!!

  27. Step Six • Divide the top (numerator) by the bottom (denominator) and answer the problem. 500 pumpkins = 500 pumpkins 1

  28. Now try for yourself… • How many centimeters are in 30 inches if there are 2.54 centimeters in one inch?

  29. Were you right? • Known = 30 inches • Unknown = centimeters • Conversion factor = 1 inch 2.54 cm 30 inches 2.54 cm = 76.2 cm 1 inch 1 There are 76.2 cm in 30 inches

  30. Now try a more complicated problem… • How many Kilometers are in 30,000 millimeters? There are 2 conversion factors • Remember to use conversion factors. Even though we know we can just move decimal points, there is a bigger lesson to be learned!

  31. Were you right? • Known = 30,000 mm • Unknown = Kilometers • Conversion factors = 1000mm1000 m 1 m 1 Km 30,000 mm 1 m 1 Km = 0.03 Km 1000 mm 1000 m There are 0.03 Km in 30,000 mm Like units are always diagonal

  32. The most complicated problem… • How many Km/h are in 15 m/s? There are 2 conversion factors Fractions!!!!!!! Only one number and one unit per block!!!!!!!!!!

  33. Were you right? = 54 km/h • Known = 15 m/s • Unknown = km/h • Conversion factors = 1000m3600 s 1 km 1 h = 1 s 15 m 1 s 15 m 1 km 1000 m 3600 s 1 h 54000 km 1000 h Remember: only one number and unit per block Like units have to be diagonal!!

  34. The most complicated problem… • How many Km/h are in 30 m/s? There are 2 conversion factors Fractions!!!!!!! Only one number and one unit per block!!!!!!!!!!

  35. Were you right? • Known = 30 m/s • Unknown = km/h • Conversion factors = 1000m3600 s 1 km 1 h 30 m 1 km 3600 s = 108,000 Km 1 s 1000 m 1 h 1000 h Answer: 108 km/h Remember: Like units have to be diagonal!!

  36. The most complicated problem… • How many m/s are in 30 km/h? There are 2 conversion factors Fractions!!!!!!! Only one number and one unit per block!!!!!!!!!!

  37. Were you right? • Known = 30 km/h • Unknown = m/s • Conversion factors = 1000m3600 s 1 km 1 h 30 km 1000 m1 h = 30000 m 1 h 1 km3600 s3600 s Answer: 8.3 m/s Remember: Like units have to be diagonal!!

  38. Important Ideas to Remember… • The key to factor label is the cancellation of units. • Always identify the known, unknown, and conversion factors in the problem. • Only one number and one unit per box!!!!! • Like units are always diagonal from one another. • Unknown is placed in first column. The rest of the columns are conversion factors. • m/s km/h mph are all fractions!!!

  39. Scientific Notation

  40. Why is Scientific Notation Important??? • Scientific notation makes it easier to work with very large numbers or very small numbers. • Mass of earth = • 6000000000000000000000000 kg • 6 x 1024kg • 6 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 x10 kg

  41. Scientific Notation on Your Calculator • Most calculators now have a key on them for doing scientific notation. Look for one of the following... • EXP (most Casio calculators) • EE (most TI calculators, and you might have to use the 2nd function key to use it) • 10x • S.N. • Do NOT use the "hat" symbol on your calculator to enter scientific notation (eg. 4.5 x 10^5). • Your calculator will treat this as two separate numbers, and you will get some calculations wrong because of it (it screws up the proper order of operations).

  42. Now try these…. • Write 3,564,000 in scientific notation. • Write 0.0043 in scientific notation. • Remember only one number in front of the decimal point!!!

  43. Were you right? • 3.564 X 106 • 4.3 X 10-3

  44. Scientific Notation • 5.0 x 10 –3 2.5 x 10 -1 • 5.05 x 10 3 2.5 x 10 -2 • 8.0 x 10 –4 2.5 x 10 -3 • 1.0 x 10 3 5.0 x 10 2 • 1.0 x 10 6 5.0 x 10 3

  45. Standard Notation • 1500 0.335 • 0.0015 0.00012 • 0.0375 10,000 • 375 0.0000001 • 220,000 400000000

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